This invention relates in general to multi-channel communication systems and, more particularly, to equalization of the channels within such multi-channel communication systems.
It is often desirable for the individual channels in a multi-channel communication system to be matched with one another as closely as possible. Mismatched channels are known to significantly degrade performance in several applications. For example, multi-channel radar systems which employ adaptive cancellation techniques to substantially reduce electronic interference are adversely affected by channel mismatching. Such adaptive cancellation in the spatial domain uses a weighted sum of channel output signals wherein the weights are adaptively computed to form spatial nulls in the directions of arrival of interference signals. In this manner, the undesired effects of the interfering signals are significantly ameliorated. This adaptive cancellation technique is also referred to as adaptive beamforming.
The depth of the null achieved in adaptive cancellation determines the degree of rejection of interference. The maximization of null depth has become increasingly important in communication applications such as radar systems where rejection of interference is critical. Unfortunately, when a null is formed by the weighted sum of several channels, as is the conventional practice, the depth of the null is limited by mismatching of the characteristics of the channels. If the mismatch among the channels is caused by the overall phase shift and/or variations in the gain of the various channels, then the adaptive weighting algorithm employed in the adaptive cancellation technique should compensate for this. However, this compensation is inherently limited by the degree to which the phase shift and gain characteristics of the individual channels track each other across the signal bandwidth. Adaptive cancellation of these sub-band variations can be achieved. Unfortunately however, to accomplish such adaptive cancellation, a prohibitively large increase in adaptive weighting complexity and adaptation time is typically required.
One approach to solving this problem is to provide channels which are matched to the appropriate level prior to commencing adaptive processing. However, beyond certain matching levels, the expense of fabricating such matched channel again becomes prohibitive. Even if such an extremely expensive approach is successfully implemented, the resulting matched channel apparatus is subject to the de-matching effects of temperature variations and component aging.
A number of methods of sub-band mismatch calibration have been tried in an effort to address the problems discussed above. For example, Pohlig in his publication, Pohlig, S. C., "Digital Signal Processing For Spaced-Based Radar", Project Report SRT-30, Lincoln Laboratory, Lexington, Mass., September 1988, discusses three methods for measurement and equalization of sub-band mismatch. Pohlig's first method involves measuring the frequency responses of a reference channel, H.sub.0 (.omega.), and a number of object channels, H.sub.i (.omega.), by sequentially injecting single-tone test signals at equally spaced frequencies and measuring the phase and gain of each channel at each frequency. The frequency spacing must meet some minimum based on the length of the expected correlation response of the channel. The span of frequencies must cover the interval over which sub-band balance is required. The frequency responses are transformed into autocorrelation and cross correlation sequences in the time domain. The autocorrelation and cross correlation sequences in the time domain are formed into matrix equations which are then solved for the equalizing filter impulse responses.
Pohlig discloses a second approach wherein white noise is injected into all channels of a multi-channel system including both the reference channel and the object channels. At predetermined intervals, a single sample, x.sub.0 (n.sub.0), is collected from the output of the reference channel while a sequence of N.sub.g samples, x.sub.i (0 . . . N.sub.g -1) is collected from each object channel. Several iterations of this process result in data samples which are processed into the autocorrelation and cross correlation function estimates. As with the Pohlig method first discussed above, this method also requires that the autocorrelation and cross correlation functions be placed in matrix form and solved for the equalizing filter impulse responses, g.sub.i.
Pohlig also discusses a third approach which is similar to the second approach except that the excitation signal which is injected into the reference channel and the object channels is a simultaneous composite of the multiple tones used in the first approach rather than a white noise signal.
Unfortunately, each of the three approaches discussed above depend on matrix inversion techniques which consume vast quantities of computational resources. This tends to make implementation of such sub-band mismatch calibration methods very slow. Moreover, additional computational difficulties may be encountered in the second approach because there is no guarantee that the resultant matrix will be well-behaved in the mathematical sense.